Explanation Formula used: Formula for Integration by parts : ∫ u d v = u v − ∫ v d u Calculation: The given differential equation is v ″ ( x ) = x e x . Take the indefinite integral of both sides, ∫ v ″ ( x ) d x = ∫ ( x e x ) d x v ′ ( x ) = x ( ∫ e x d x ) − ∫ ( ∫ e x d x ) d x ( by Integration by parts ) = x e x − ∫ e x d x v ′ ( x ) = x e x − e x + C 1 Again integrate the above equation, ∫ v

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Differential Equations

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Chapter D1.1, Problem 22E

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To find: The general solution of the differential equation v″(x)=xex .

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Chapter D1.1, Problem 21E

Chapter D1.1, Problem 23E

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Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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The general solution of the differential equation v ″ ( x ) = x e x .

Solution Summary: The author explains how to find the general solution of the differential equation v′′(x)=x

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To find: The general solution of the differential equation v″(x)=xex .

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Chapter D1 Solutions